Parallelization of DQMC simulation for strongly correlated electron systems

摘要

Determinant Quantum Monte Carlo (DQMC) simulation has been widely used to reveal macroscopic properties of strong correlated materials. However, parallelization of the DQMC simulation is extremely challenging duo to the serial nature of underlying Markov chain and numerical stability issues. We extend previous work with novelty by presenting a hybrid granularity parallelization (HGP) scheme that combines algorithmic and implementation techniques to speed up the DQMC simulation. From coarse-grained parallel Markov chain and task decompositions to fine-grained parallelization methods for matrix computations and Green's function calculations, the HGP scheme explores the parallelism on different levels and maps the underlying algorithms onto different computational components that are suitable for modern high performance heterogeneous computer systems. Practical techniques, such as communication and computation overlapping, message compression and load balancing are also considered in the proposed HGP scheme. We have implemented the DQMC simulation with the HGP scheme on an IBM Blue Gene/P system. The effectiveness of the new scheme is demonstrated through both theoretical analysis and performance results. Experiments have shown over a factor of 80 speedups on an IBM Blue Gene/P system with 1,014 computational processors.